Question

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Explanation:

Relate coefficients to factors

$$ x^2 + bx + c = (x + m)(x + n) = x^2 + (m + n)x + mn $$

Equate corresponding terms

$$
LATEXBLOCK0
$$

Analyze signs of m and n

Using the given conditions that \(c > 0\) (positive) and \(b < 0\) (negative):

$$
LATEXBLOCK1
$$

Answer:

• m and n are both positive.
• m is positive and n is negative.
• m is negative and n is positive.
• m and n are both negative. (Correct answer)